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Multilevel latent class analysis
Mplus Discussion
Multilevel Data/Complex Sample
Sven De Maeyer
posted on Monday, March 29, 2004 - 9:01 am
I would like to inform if it is possible to include a latent class variable in a multilevel model. For instance in school effectiveness reseach: some characteristics could possibly distinguish 5 classes of schools. Would it be possible to use this latent class variable to predict student outcomes at the lowest level. Or is this impossible? If so, are there references to check for more details about this option?
thank you for the information
Linda K. Muthen
posted on Monday, March 29, 2004 - 9:24 am
Version 3 of Mplus can estimate multilevel mixture models. The Version 3 User's Guide will describe how to set these models up.
posted on Monday, March 29, 2004 - 6:32 pm
Hi Linda,
In order to estimate multilevel mixture model (that is, multilevel model with finite mixture random component), I need the base package, the multilevel addon, and the mixture addon, am I correct about this? Thanks!
Linda K. Muthen
posted on Tuesday, March 30, 2004 - 7:19 am
You would need the combination add-on to estimate a multilevel mixture model.
Joyce T.
posted on Monday, April 04, 2005 - 6:36 am
I'am running a multilevel model (using ML) which contains 20 dependant variables, 12 independant variables and 3 continuous latent variables.
I would like to know how mplus compute the degrees of freedom for both, the Chi-square test of model fit and the Chi-square test of model fit for the baseline model.
posted on Wednesday, April 06, 2005 - 3:03 am
The degrees of freedom is the number of parameters in the H1 model minus the number of parameters in the H0 model. The chi-square test of model fit for ML uses as H1 a model with free means, and free variances and covariances for both within and between. The baseline model is a model of free means and variances for between and within.
Ann-marie Faria
posted on Friday, September 25, 2009 - 7:42 am
I am working on a multi-level LCA in a school-based data set. The variables of interest are 1) parent involvement (a child level variable) and 2) classroom quality (a classroom level variable). The ultimate goal is to use the latent classes as independent variables to predict child outcomes such as school readiness.
1) One question that has come up in our discussions is how to deal with important covariates (such as maternal education, child age, child sex, child ethnicity). I was wondering if you could speak to the differences between a) including the covariates in the model that estimates the latent class memberships vs. b) running post-hoc ANOVAS to examine the distribution of the profiles on these important covariates.
2) Also I am interested in how using the Latent Classes as independent variables to predict other outcomes would shift class memberships. Does this often happen when adding a predictive step into LCA/LPA models?
3) Finally we are using a national database with sampling weights, will weighting the data influence the LCA/LPA outcomes?
Thank you so much for your time
Linda K. Muthen
posted on Friday, September 25, 2009 - 11:04 am
1. Generally it is best to estimate the full model simultaneously. See the following paper which is available on the website for further information:
Relating latent class analysis results to variables not included in the analysis. Submitted for publication.
2. If you add outcomes other than the original set, this will most likely change class membership and perhaps it should. See the following related paper which is available on the website:
Muth�n, B. (2004). Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data. In D. Kaplan (ed.), Handbook of quantitative methodology for the social sciences (pp. 345-368). Newbury Park, CA: Sage Publications.
3. You can and should include complex survey data features in the analysis. See the user's guide under complex survey data to see the options available in Mplus.
Ann-marie Faria
posted on Friday, September 25, 2009 - 11:18 am
Thank you for your quick reply and for the references.
Best, Ann-Marie
Ann-marie Faria
posted on Monday, May 10, 2010 - 12:03 pm
Hello Linda-
I have two follow up questions for the multilevel LCA we are working on.
1) Standardized Scores: Do you suggest running the models with standardized continuous indicators? Or is it acceptable to keep the indicators of profiles in their original metric (even if variances are different among indicators?)
2) Predicting Outcomes from Profile Membership: Also, for estimating the relationship between different profiles and an outcome (say literacy achievement) we have been including the outcome of interest as an indicator of profile membership. We then ran a Wald statistic to examine profile differences on the mean estimates of the outcome. Is this how you would suggest estimating profile differences on an outcome?
Thank you-
Linda K. Muthen
posted on Tuesday, May 11, 2010 - 9:48 am
1. I would not standardize.
2. Yes.
Andre Plamondon
posted on Saturday, June 19, 2010 - 12:40 pm
I have a question regarding a multi-level LCA too.
I am using a sample of twins in which I would like to identify the genetic-environmental etiology of class membership. I also have predictors at the within and the between level.
Since regressing the measured environmental variable doesn't seem to modify the ACE results (as seen in Turkheimer et al., 2005), I would like to use another strategy developed by Rasgach, O'Connor and Jenkins in which the genetic resemblance is a fixed effect.
Although I think this strategy is the best, I'm not sure how to actually bring the equation in a Mplus input.
The equation is :
y(ij) = Beta(o) + u(j) + e(ij) + g(ij)
Basically, the only thing that changes from a regular multilevel model is the g(ij) which is the genetic effect for the child (i) in the j'th family which varies for all individuals according to behavior genetic assumptions (it can be used with complex family pedigrees). I am wondering what do I write in the input. I think they use a single group to do the analyses and it departs from the multiple group analyses I am used to with twin samples.
Maybe the paper would make it clearer :
The equation is on page 8.
Bengt O. Muthen
posted on Sunday, June 20, 2010 - 11:31 am
Page 8, bottom, suggests that a covariance for the g(ij) term is a function of known constants. This reminds me of "QTL" modeling which is shown in the UG ex 5.23. This UG example shows how to use the Constraint= approach to moderate a covariance using read-in values. Perhaps that is a path towards doing what you want.
Ann-marie Faria
posted on Friday, June 25, 2010 - 10:48 am
In running the multi-level LPA I mentioned earlier, we see from the output that the means of the indicators in the level 2 profiles are constrained to be equal across profiles. It appears that this is the default in Mplus.
Is it possible simultaneously estimate a latent profile of level 1 (child level variables) and a latent profile of level 2 (classroom level variables) without the level 2 means being fixed across level 2 profiles?
I attempted to override this estimation with starting values, but am getting repeated errors messages:
The following MODEL statements are ignored:
* Statements in Class %CB#1% of MODEL CB on the BETWEEN level:
* Statements in Class %CB#2% of MODEL CB on the BETWEEN level:
One or more MODEL statements were ignored. These statements may be incorrect.
Do you have any suggestions?
Thank you again,
Linda K. Muthen
posted on Friday, June 25, 2010 - 10:56 am
Please send the full output and your license number to
Robert Urban
posted on Friday, December 17, 2010 - 10:12 am
Dear Dr. Muth�n,
I want to perform LCA on a complex dataset (teachers were rating students), and want to control for clustering effect. However I cannot define Type=complex, since this is already done with Type=mixture.
How can I use the clustering or stratification options in this type of analysis?
Thanks a lot.
Linda K. Muthen
posted on Friday, December 17, 2010 - 10:43 am
You can use TYPE = MIXTURE COMPLEX;
Michelle Maier
posted on Friday, March 11, 2011 - 8:37 am
I am working on a two-level LCA where the variables of interest include both child-level (observed child interactions) and class-level variables (classroom quality). I have specified two classes at each level. I would like to see if the resulting four profiles differ on child-level school readiness outcomes. Is there a way to get an outcome mean for each profile? I am only able to get two means (one for each of the within classes) rather than four means (one for each of the four profiles).
Thank you!
Bengt O. Muthen
posted on Friday, March 11, 2011 - 9:49 am
Take a look at the 2010 Henry-Muthen article in the SEM journal. For the models of figures 1-4 the between classes only make the within classes more or less likely but don't change the profiles of the observed items. In contrast, for figure 5 and on there are item-specific differences across the between-level classes so that would give the profile differences you expect.
K Frampton
posted on Wednesday, March 16, 2011 - 11:23 am
I am running a multilevel LPA with continuous parenting indicators, with children nested within families. My goal is to identify parenting profiles, observe how they differ across various factors (mainly SES), and then use profile membership to predict a distal outcome (children's prosocial skills) in interaction with SES.
I first fit the model in a single level, and then in a multilevel. 4 classes were identified. Entropy is .86.
I then added covariates of interest(e.g., age of child, SES variables), to identify what distinguishes these groups. When I do this, the structure of the classes changes significantly. I know this is because of measurement variance issues. When I regress parenting indicators on covariate(s) in a single level, it improves the fit of the model. However, in a multilevel, when I do the same thing, computation time was + 2 hours, and it did not converge.
Any suggestions on how to get around this measurement variance issue in a multilevel? Because entropy is high, is it feasible in a multilevel framework to save the classes identified and then work with them as an observed variable, as you might do in a single level?
Also, with all this in mind - how would you suggest answering my final question - how SES X profile predicts a distal outcome?
I am grateful for any recommendations. Thanks.
Bengt O. Muthen
posted on Wednesday, March 16, 2011 - 4:30 pm
It sounds like you have measurement non-invariance and that you add direct effects from covariates to indicators to take this into account. Note that you cannot identify a model with all direct effects.
To see your multilevel problem, you would have to send your input, output, data, and license number to
SES X profile influencing a distal can be handled by distal regressed on SEM with different slopes in the different profiles.
IYH Boon
posted on Monday, June 27, 2011 - 12:58 pm
Are there any examples/code snippets available for situations like the one K Frampton describes, above, where the goal is to (1) identify latent profiles at level two and (2) relate these profiles to a distal outcome observed at level one?
I'm working on a similar problem and am unsure about how to specify the model statement.
Thanks in advance for the help,
Bengt O. Muthen
posted on Monday, June 27, 2011 - 5:32 pm
I don't think we have that in script or paper form, but you would work along the lines of the below. This creates a between-level (say school) latent class variable cb from the between-level z indicators and cb influences the means of the random intercept for the distal outcome d (which is say a student variable varying on both within and between), which is how the cb influence carries over to the student's distal outcome.
Between = z1-z10 cb;
classes = cb(2);
d on x;
I don't think you have to say more in MODEL because the z means vary across the cb classes as the default, and so does the d mean, where on between d is the random intercept in the regression of d on x.
Hope this start helps.
Junqing Liu
posted on Thursday, August 25, 2011 - 12:50 pm
I am new to Mplus and LPA. I am working on a two-level LPA in a workforce data set. The variables of interest are 1) organization culture (a level 2 latent variable based on five level 2 continuous indicators) and 2) worker demography and practices and (level 1 observed variables). The goal is to use the latent classes as independent variables to predict workers' practice such as using a type of therapy.
1)One question is do i need to run the LPA first to get the classes(say there will be 2 or 3 categories)before including the latent class variable into the final model to predict the worker outcome?
2) In the final model using the org. culture class membership to predict worker outcome, do i need to include the observed organization id as a predicting variable to declare this is two-level model?
3) What is the output of the final model? Is it separate regression models for each category of org. culture? Or is it one regression?
4) Is there any empirical research reference on cross-sectional multilevel LPA analysis that I can read?
Many thanks!
Bengt O. Muthen
posted on Thursday, August 25, 2011 - 5:29 pm
1) Although not necessary, it's a good idea.
2) Orginization would be your Cluster= variable - see UG.
3)-4) You should read
Henry, K. & Muth�n, B. (2010). Multilevel latent class analysis: An application of adolescent smoking typologies with individual and contextual predictors. Structural Equation Modeling, 17, 193-215.
which you can find on our web site.
Junqing Liu
posted on Friday, August 26, 2011 - 1:48 pm
Hi Bengt,
This is extremely helpful!
I can compare different LPA models and pick one that fits the best as the final latent profile model to do further analysis. I have some follow-up questions about the further analysis.
1.How common is it to use the latent profile variable as a predictor along with other covariates, rather than as a dependent variable?
2. If it is common, then should a level 1 latent profile variable be included as a regular categorical covariate (along with other level 1 and level 2 predictors) to predict a level 1 outcome or the way to included it depends on how the latent profile variable is modeled such as a two-level latent profile model with level 2 factor on random latent class intercepts and level 2 factor on random latent class indicators?
3. Is there any empirical research reference on using multilevel latent profile variable as predictor that I can read?
Thank you for your patience with my long-windedness.
Bengt O. Muthen
posted on Saturday, August 27, 2011 - 12:01 pm
1. It is getting more used now that software is available for easy use. There are papers on our web site showing this. But I would not say that it is common yet.
2. A latent class variable should be included as a predictor if substantive theory warrants that. Note, however, that you don't say "y ON c" (for a distal outcome y), but Mplus lets the y means change over the latent classes.
3. I have not seen multilevel latent profile used as a predictor yet in the literature, but there is nothing precluding it. The approach used in Henry & Muthen can easily be expanded to that using Mplus.
Junqing Liu
posted on Friday, September 09, 2011 - 6:56 am
Thanks, Bengt. This is very helpful.
I tried the following three-class two-level LPA of org. culture. However, the output does not include results on latent classes. All the results are about correlations and covariance. The five latent indicators are the mean score of scales and the value ranging from 1 to 5.
1) How may i change the following syntax to get output on latent classes?
2) Is it ok to use the mean of scales as latent indicators? Or is it better to use the items within the scales as indicators?
Thank you very much.
Usevariables = l_coh_ag L_aut M_Coll M_FocOut M_RoCn ORGID;
Classes = c(3);
Within=l_coh_ag L_aut M_Coll M_FocOut M_RoCn;
type = mixture twolevel;
starts=20 10;
Bengt O. Muthen
posted on Friday, September 09, 2011 - 7:11 am
Please send your output to support.
Junqing Liu
posted on Tuesday, September 13, 2011 - 12:49 pm
Thanks, Bengt and Linda. The technical problem is solved.
I have a couple of questions related to the results of the two-level model i mentioned earlier.
1) Are tech 11 and tech 14 applicable to a two-level LPA model? If so, when the LMR p value of tech 11 is not but the p of tech 14 is significant, should i pick a K as oppose to a k-1 class model?
2) The BIC and AIC of the two-level model are smaller than those of a single level model, but not by much (e.g. the adjusted BIC is 2542.96 for the two-level model and is 2559.12 for the single level model). In this case, should i still choose the two-level model?
3) What the following specification means, especially C#1 WITH C#2?
Thank you very much!
Tihomir Asparouhov
posted on Tuesday, September 13, 2011 - 5:39 pm
1) In principle tech14 is more reliable however you might also want to look at BIC and AIC for the two models.
2) You should also consider the size of the variance on the between level and see if it is significant. Note also that the performance of BIC would depend on the number of clusters (two-level units) which drives the asymptotics. Ultimately a simulation study would show if AIC and BIC are useful in this context. This is not well studied.
3) These are the interaction parameters in a log-linear model for contingency tables. For example in
these are the lambda_IJ parameters.
Tihomir Asparouhov
posted on Tuesday, September 13, 2011 - 7:32 pm
Actually the answer to #3 above is not correct at all. Here is the correct answer.
C#1 and C#2 are alpha1j and alpha2j in formula (4) in
These are normally distributed random effects that vary over clusters and allow the class proportions to change over clusters. The covariance term C#1 WITH C#2; is just the covariance between the two random effects and C#1; C#2; are the two variances.
Mary Campa
posted on Thursday, September 15, 2011 - 4:40 pm
Hello Dr. Muthen,
I am reading your paper with Dr. Henry (2010, SEM 17m 193-215)and trying to replicate the analysis titled: Three classes at level 1, Two classes at level 2 random effects model: nonparametric approach (Model 4a from Table 1).
I am using 4 classes at level one but otherwise the model statements are the same. However, I continue to get this error message:
** ERROR in MODEL command
Unknown class model name CW specified in C-specific MODEL command.
I am not sure what I am missing?
Thank you for your assistance.
Bengt O. Muthen
posted on Thursday, September 15, 2011 - 6:00 pm
This can only be answered if you send the output to support.
Junqing Liu
posted on Friday, September 16, 2011 - 9:03 am
Thank you very much, Tihomir.
I have a couple follow up questions regarding the interpretation of c#1 and C#2.
1) Does the within level means of c#1 means the random intercept of c#1 as compared to c#3? What dos a significant P value of the within level means of c#1?
2) What does a non-significant p value of the between level variance of c#1 mean?
3) Regarding your earlier response on examining the significance of between level variance, should i do a log likelihood ration test of the one level and two level model, or should i use the p value that mention above, the p value of the between level variances of c#1 and c#2?
Thanks again!
Bengt O. Muthen
posted on Friday, September 16, 2011 - 9:41 am
1) Yes. That p-value is typically not of interest because it tests that the logit is zero which with 3 classes is not a meaningful point.
2) That indicates that there is zero between-level variance for class 1.
3) Neither test is optimal because of testing variances at zero, the border of the admissible parameter space. I would just leave them as is and report them.
Friedrich Platz
posted on Thursday, January 05, 2012 - 6:26 am
Happy New Year!
I hope, you had a great holidays! I'm a beginner in the field of multilevel analysis with a lot of questions. First, my aim is to reveal a typology on musicians who were rated by audience members.
I have read your very intersting and inspiring paper (Henry & Muthen, 2010). First of al, I have some questions about your paper which could help me, solving some misunderstandings:
1) To which item or construct does your cluster variable, named LEAID, refer to?
2) It would be much easier to follow your steps, reported in your article, if I could run your code on the dataset. I wrote to Mrs. Henry, but she advised me to simulate such a dataset by Monte Carlo technique. Unfortunately, I am not able to do this. How does it work?
3) I would like to use a model for my own dataset that is the same as presented in Figure 7 (multilevel latent class model � non parametric approach with level 2 factor on random latent class indicators). Would you give me a hint how to write this in MPLUS-code?
4) The final model seems also be attractive to me. But it is hard to understand your reported code without any comments on it. Especially the lower part (model constraint). I would be happy, If you could give us some comments on the code.
I would be very happy, if you could help me answering these questions.
Thank you!
Linda K. Muthen
posted on Thursday, January 05, 2012 - 12:28 pm
You can look at Examples 10.6 and 10.7 in the user's guide. These are similar to what is done in the Henry and Muthen paper and there are data available with each example. A note of caution, if you are a beginner in multilevel analysis, starting with a multilevel mixture model may not be a good idea. Studying both multilevel and mixture modeling as a first step is a good idea.
Friedrich Platz
posted on Thursday, January 05, 2012 - 1:00 pm
Thank's a lot. Which literature would you recommend for an good introduction into These topics?
All the best!
Linda K. Muthen
posted on Thursday, January 05, 2012 - 1:18 pm
You can see our Topics 5, 6, 7, and 8 course handouts which cover these topics and contain references.
Friedrich Platz
posted on Thursday, January 05, 2012 - 1:26 pm
Thank you!
Angela Urick
posted on Thursday, January 19, 2012 - 12:46 pm
I�m working on a two-level LCA (types of teachers in schools with types of principals) with a cw and cb that have different indicators (I have labeled them uw�s and ub�s below). These two sets of indicators have dichotomous and continuous measures. Finally, I want to regress cw on cb with a random intercept (similar to ex. 10.7). Here is my basic code:
CATEGORICAL = uw 1 - uw15 ub1 - ub13;
CLASSES= cb(3) cw(4);
WITHIN= uw1 � uw30 x;
BETWEEN= cb ub1 - ub30 w;
cw on x;
cb on w;
cw#1 � cw#3 on cb;
[uw1$1 � uw15$1]
[uw16 � uw30]
[uw1$1 � uw15$1]
[uw16 � uw30]
[uw1$1 � uw15$1]
[uw16 � uw30]
[uw1$1 � uw15$1]
[uw16 � uw30]
Here are my questions:
1. Is a LRT (TECH 11, 14) possible for this model with different indicators for cw and cb? If not, how would you suggest that I asses class fit?
2. Theoretically, there is a two-way relationship between cw and cb, how would you suggest that this be modeled?
Bengt O. Muthen
posted on Thursday, January 19, 2012 - 8:57 pm
1. No. It is an open research question on how to determine number of classes in a multilevel setting such as this. The ordinary BIC, for example, may not be the best approach. Interpretability can be helpful.
2. The relationship between cw and cb is captured by the between-level statement
cw#1 � cw#3 on cb;
where the cw random intercepts are influenced by cb.
Angela Urick
posted on Saturday, January 21, 2012 - 10:33 am
Thank you, Dr. Muthen.
Angela Urick
posted on Monday, January 30, 2012 - 1:05 pm
Good afternoon, Dr. Muthen,
I have another question in reference to the model mentioned above. In the results, the means of the level 1 indicators (uw/u) vary across classes as expected. However, the means of the level 2 indicators (ub/z) are the same across all classes. I ran cb as a single level LCA�there should be three different classes. Why would these means remain the same across the between level classes? Do I need to free the between level indicators or make other edits to the code?
Thanks again, Angela
Bengt O. Muthen
posted on Monday, January 30, 2012 - 8:26 pm
Model cb:
and then mention the intercepts of the ub indicators in each of the cb classes.
Angela Urick
posted on Tuesday, January 31, 2012 - 10:19 am
Thanks, it worked.
Mary Campa
posted on Saturday, May 26, 2012 - 12:13 pm
I am building a model similar to the Henry & Muthen, 2010 model 2, a two-level random effects LCA. I have selected a four-class model as best fitting. My question is about the between-level variances produced by this code:
I used starting values to switch the ordering of the classes and the estimates and standard errors of the between-level variances (C#1 -C#3) changed. For example, on the initial run, the variance in class 2 was significant but on the next run the variance for the same class (although now a new number) was not. This happened for multiple classes, where the parameter estimates changed based on what class I selected as the reference.
My understanding from the Henry & Muthen paper is that these parameters represent the between-level variance in the class membership. The classes (proportions, probability of indicators) remains the same regardless of which is the reference class so I am not clear why these are changing.
Does this suggest there is something wrong with my model or am I wrong in the interpretation?
Thank you for your help.
Bengt O. Muthen
posted on Saturday, May 26, 2012 - 12:42 pm
The multinomial regression has the coefficients at zero for the last class, the reference class. The between-level variance components add to the coefficients for all but the last class. It makes sense that the size and SEs of these variance components change when you change the order of the classes because it is all relative to the reference class.
posted on Friday, June 08, 2012 - 3:44 pm
Hi Dr. Muthen,
Thank you so much for your help in advance.
I'm running a two level LCA and latent variable and independent (treat) is school level, and dependent variable is student level.
According to the Number of clusters: 32, isn't the sum of latent classes supposed be 32 as well? But, the results show latent variables were converged by student level not school level like below:
Class Counts and Proportions
1 1437 0.53720
2 1238 0.46280
CLUSTER = school;
BETWEEN = treat c;
CLASSES = c(2);
TYPE IS TWOLEVEL random MIXTURE;
dv on treat;
dv on treat;
Bengt O. Muthen
posted on Friday, June 08, 2012 - 8:36 pm
Although the latent class variable is a between-level variable (varying across schools only), the class counts and proportions printed say how many students are in each class. But there are only 32 schools and the latent classes refer to them.
posted on Friday, June 08, 2012 - 11:29 pm
Thank you so much for the prompt response.
posted on Thursday, July 05, 2012 - 6:09 am
Dear Prof Muthen,
I fit multilevel finite mixture modelling for count data. I want to get variances across classes in level 1 and level 2. I run the model with this code:
y on x1;
y on x1;
y on w;
y on w;
With this model, Mplus only give me one number of variance across classess and level. How I have to intrepret these variances? Can Mplus 6.1 reveal variances across classes and level?
Thanks very much for your help
Linda K. Muthen
posted on Thursday, July 05, 2012 - 11:07 am
Please send your output and license number to
xiaoshu zhu
posted on Wednesday, July 25, 2012 - 10:56 am
I have a question regarding the class membership at the group level.
I followed the codes for the non-parametric MLCA in Henry and Muthen (2010) and specified a model with two student LCs and three group LCs. The output showed that some groups were assigned to two group LCs, simultaneously.
How can we deal with this problem? Should we decide the group class membership based on the one with largest proportion of students within the group?
Thanks in advance!
Linda K. Muthen
posted on Thursday, July 26, 2012 - 11:59 am
Please send the output and saved data along with your license number to
. Point to specifically what you see as the problem.
Mike Todd
posted on Sunday, January 20, 2013 - 5:14 pm
Hello there:
We have a multilevel dataset (individuals nested with census tracts) that we would like to use in a multilevel latent profile analysis.
The census tracts (Level 2 units), and in turn, the individuals (Level 1 units) can be grouped into two categories. What we are wondering is if how/if measurement invariance across the two categories can be tested for in a multilevel LPA/LCA. Would we test this in the same manner that we would for standard "single-level" LPA? If not, can you point us to a relevant approach that could be applied to results generated by Mplus?
Thanks so much!
Bengt O. Muthen
posted on Sunday, January 20, 2013 - 5:35 pm
It sounds like you have an observed grouping variable on level 2. This can be handled by defining a between-level latent class variable that is exactly the same as the grouping variable. See UG ex 7.24 for how this is done in the single-level case. The between-level latent class variable has to be declared on the Between = list as in UG chapter 10. Then you can specify and test various degrees of measurement invariance across these between-level classes.
Mike Todd
posted on Monday, January 21, 2013 - 9:11 am
Great! Thanks, Bengt!
Karoline Bading
posted on Saturday, March 15, 2014 - 9:26 am
first part:
hello everybody
i am running a latent analysis with complex survey data on 9 items aiming at political alienation and willingness to participate in the democratic process.
in my early steps i ran the analysis without type = complex mixture (only type = mixture) and it turned out that a 3- and 4-class solution seemed the most reasonable solutions (log-likelihood based fit indices were all pretty sobering, but interpretation was consistent with substantive theory of the construct).
later i realised i should be using type = complex mixture, since the data is clustered with n(cluster)= 27 and differing cluster sizes. hence, i re-ran the analysis for 3,4 and 5 latent classes.
what struck me was, that the estimates did not change at all for the 3 and 5 class solutions, but changed considerably for the 4 class solution, which was the best model interpretation-wise when using only type = complex and now unfortunately is far less sensical.
Karoline Bading
posted on Saturday, March 15, 2014 - 9:27 am
second part: (sorry for the long message!)
how is that possible, that 3 and 5 class solutions did not change, but the 4 class solution did?
estimator is mlr, which i assume somehow weights with cluster-size?
could that be "playing against" my beloved 4 class solution, because one the classes is quite small in comparison to the other 3. maybe if people in this class come from cluster units with a small weight (due to small cluster unit size), this class cannot be detected well enough?
as you can tell, i only have a very vague understanding of how the estimators work. i apologize for painful stupidity in my thoughts expressed above.
do you have any recommendations for chosing an estimator when using type = complex mixture. ive heard there are different options: mlr, uls ...
are there any paper where i could look things up?
thanks so much for help!
Linda K. Muthen
posted on Sunday, March 16, 2014 - 11:54 am
Unless you have weights, your classes should not change when adding COMPLEX. Perhaps you are not replicating the best loglikelihood in all analyses. Or perhaps the order of the classes changed. If you can't see the problem, send the relevant outputs and your license number to
The only estimator available for TYPE=COMPLEX is MLR.
Please limit future posts to one window. If they are longer than that, they are not appropriate for Mplus Discussion.
Karoline Bading
posted on Sunday, March 16, 2014 - 12:33 pm
thanks for the answer.
i want to run the blrt but i am using type = complex mixture option. if i compare the 5 class solution using type=complex mixture to the 5 class solution using only type = mixture, estimates dont change and p-values do, but only slighty.
would it be acceptable to run the blrt using type = mixture even though the data is in fact clustered?
Linda K. Muthen
posted on Monday, March 17, 2014 - 2:52 pm
I would not use BLRT using TYPE=MIXTURE if you have clustered data. I would use BIC.
giulia peruzzi
posted on Tuesday, April 15, 2014 - 9:11 am
hi, i'm running this multilevel latent class model:
Names are
indir INDIR1 INDIR2 id GENERE REGOLARE CITT CITT2 NUCLEO1 NUCLEO2
HISEI SP_SCOL sp_sc_d cod_scu;
Missing are all (-9999) ;
auxiliary are id;
usevariables are GENERE REGOLARE CITT2
categorical are GENERE REGOLARE CITT2
Classes = CB(2) CW(3);
within = GENERE REGOLARE CITT2
between = CB;
cluster = cod_scu;
Type= Mixture Twolevel;
CW on CB;
And i have two questions:
1) i have different thresholds' estimates in the same within classes, i.e.
thresholds' estimates of latent class 1 1 are different from these of latent class 2 1.
Is it correct?
2) How can i calculate thresholds' estimates in probability scale?
giulia peruzzi
posted on Tuesday, April 15, 2014 - 10:08 am
I'm sorry: i forgot to say "Thanks"
Bengt O. Muthen
posted on Wednesday, April 16, 2014 - 5:57 pm
1) The thresholds vary across the between-level CB classes as the default. You should think of thresholds as a between-level quantity in line with having means appear on between in regular multilevel modeling.
2) This is tricky because the probabilities involve the random effects and therefore require numerical integration.
giulia peruzzi
posted on Tuesday, May 06, 2014 - 8:10 am
Dear Bengt, thank you for your kind reply. I would have two minor remarks just to be sure to have properly understood your comments.
1) the following is part of my output. According to your examples, the first coefficients in each group of thresholds (e.g. the pairs of GENERE$1) should be equal.
As you can see, mine are not.Is there a mistake or is there a reason I cannot see underlying this results?
Latent Class Pattern 1 1
Latent Class Pattern 2 1
2) ok, i understand, but it's very difficult interpreting characteristics of classes looking at threshold's estimates. could it be a good idea saving class probabilities and then analizing classes with descriptive statistics?
Bengt O. Muthen
posted on Tuesday, May 06, 2014 - 6:46 pm
Which of my examples are you referring to?
giulia peruzzi
posted on Wednesday, May 07, 2014 - 12:00 am
I'm sorry: not properly "your" example, actually... i'm referring to Guide's example, 10x7.
Thanks a lot
Bengt O. Muthen
posted on Wednesday, May 07, 2014 - 11:46 am
Yes, ex 10.7 has the thresholds equal across the cb classes. So you are saying you don't get that - then I would have to see your full output to Support along with your license number.
posted on Saturday, July 19, 2014 - 10:24 am
I don't think I'm finding a models similar to what I want to explore in MPlus inside the user's guide. I have 2 specific questions.
Here's goes:
-Question 1: I'm creating a multilevel latent profile model for students in classrooms. I want to see if the the random effects (intercepts) for profiles latent means, constituted by a battery of student indicators, are predicted by a level 2 latent factor for classroom environment.
Would I specify that latent factor for classroom environment in this part of the model statement?
schoolfactor by indicators
c#1 on schoolfactor
c#2 on schoolfactor
- Question 2: Finally, how would I specify a multilevel mixture model where the profile is constituted by child (level1) and classroom (level2) indicators? The profile might have measures of cognitive and social outcomes for children as well as measures of classroom environment.
Bengt O. Muthen
posted on Saturday, July 19, 2014 - 4:10 pm
Q1. You would follow the ideas in the Henry-Muthen multilevel LCA paper on our website. Declare a between-level latent class variable. On between you simply say
schoolfac BY ....;
which will give you the schoolfactor means in the different between classes.
Q2. Just declare the classroom environment variables as Between variables and include them in the BY statement.
posted on Thursday, February 26, 2015 - 3:03 am
I am running a multilevel mixture analysis with random effects. My variables are y x1 x2 x3 x4 x5.
On level 1:
Y on x1 x2 x3 x4
On level 2, I would like to identify latent classes (cb) using only the random slopes from level 1 (s1 s2 s3 s4). I do not want to include random intercept (y) as it does not make substantive sense, in my case. Following your example on the User�s Guide (example 10.2), I notice the random intercept is included as an indicator of cb. How can I specify that only the random slopes be used?
Thank you in advance for your response.
Bengt O. Muthen
posted on Thursday, February 26, 2015 - 7:27 am
What you want implies that the mean of the random intercept y would not vary across the cb classes. To specify that you would need to hold those means equal across the cb classes:
[y] (1);
[y] (1);
posted on Thursday, March 05, 2015 - 2:31 am
I posted earlier on about the multilevel analyses I am running. My further questions are:
1) Repeated measures nested in individuals is by other multilevel standards 2-level but considered 1-level model by Mplus, as I understand from the UG. In my input I specified the model as TYPE = TWOLEVEL MIXTURE RANDOM; is this correct?
2) The ICs (Bic, aBic) and entropy favour a 3-class solution but the LRT does not. So I am trying to use TECH14 to test the different class solutions by bootstrap but the model keeps running and never stops (2 days!). What could the problem be?
lrtstarts= 50 20 50 20;
3) I had done the multilevel analyses without modelling latent class in HLM. When I run this same model in Mplus, some random slope variances which were significant in HLM become NSG in Mplus. Why is this so?
4) Could this be due to nonnormale multivariate nature of the data? I wanted to change the estimator to MLM but got an error message. Is this impossible to do?
Your help with these questions will be much appreciated.
Bengt O. Muthen
posted on Thursday, March 05, 2015 - 9:42 am
1) In Mplus you can do growth as 2-level in long format or as 1-level in wide format. We recommend the latter whenever possible. So if you take the latter approach, Type=Twolevel would refer to some other clustering like students in classrooms.
2) I would simply go by BIC.
3) Perhaps you used MLR in Mplus and ML in HLM.
4) Use MLR.
posted on Thursday, March 05, 2015 - 12:33 pm
Thank you very much for your response. When I used ML as the estimator in Mplus my results were similar to that got with HLM using ML. However, there were still slight diff�rences in the p values.
Could you point me to any paper that I can reference in which the information provided by ICs, LRT and entropy were contradictory? Thank you once again for your help.
Bengt O. Muthen
posted on Thursday, March 05, 2015 - 1:18 pm
Perhaps this paper is useful:
Morgan, G. B. (2014). Mixed mode latent class analysis: An examination of fit index performance for classification. Structural Equation Modeling: A Multidisciplinary Journal, DOI: 10.1080/10705511.2014.935751
E. Cohen
posted on Monday, August 24, 2015 - 6:57 am
Dear Drs. Muth�n, I have the following multilevel LCA problem: I want to identify subtypes of related cases in a multilevel sampling context (three levels), using a set of seven categorical variables measured on levels 1 and 2 (4 L1 variables, 3 L2 variables).
Two questions:
1. Is it possible (yet) to estimate a MLCA model with latent classes based on indicators/variables measured on different levels? (Henry & Muth�n (2010) as well as other articles on MLCA look at models comprising L1 latent classes only.)
2. Is it possible (yet) in Mplus to estimate a three-level LCA (with covariates on two levels predicting class membership)? If not, is there a general estimation/data preparation strategy you would suggest (e.g., ignoring � while acknowledging � L3 clustering, or aggregating scores on L1 variable and treat them as L2 variables, then omitting L1 and shifting the level of analysis upwards)?
Thanks in advance for your help!
Bengt O. Muthen
posted on Tuesday, August 25, 2015 - 8:29 am
1. Mplus handles latent class variables on both level 1 and level 2. See for example,
the paper on our website:
Muth�n, B. & Asparouhov, T. (2009). Growth mixture modeling: Analysis with non-Gaussian random effects. In Fitzmaurice, G., Davidian, M., Verbeke, G. & Molenberghs, G. (eds.), Longitudinal Data Analysis, pp. 143-165. Boca Raton: Chapman & Hall/CRC Press.
and also
Muth�n, B. & Asparouhov, T. (2009). Multilevel regression mixture analysis. Journal of the Royal Statistical Society, Series A, 172, 639-657.
2. I think level 1 and level 2 latent class variables can have their random intercepts be predicted by level 2 and level 3 covariates.
Bengt O. Muthen
posted on Tuesday, August 25, 2015 - 8:56 am
See also UG ex 10.5 and 10.8 where you see "cb". cb can have observed level 2 indicators as well.
Vanessa Castro
posted on Friday, October 23, 2015 - 8:33 am
I ran the following LPA
Type = Mixture Complex ;
algorithm = integration;
integration = montecarlo;
Starts = 100 10;
stiterations = 10;
k-1starts = 100 10;
processors =8(starts);
c on age_oa age_ma; age_oa age_ma;
Why in the output, is the covariate (age group dummy coded for middle and older adults) listed within each factor?
Latent Class 1
Bengt O. Muthen
posted on Friday, October 23, 2015 - 3:10 pm
Because you change the status of those age dummies from covariates to variables that have parameters in the model by your statement:
age_oa age_ma;
So they are just like any other "Y" variables.
Vanessa Castro
posted on Friday, October 23, 2015 - 3:22 pm
Thank you Dr. Muthen for your response.
I had to include that statement for the model to run, otherwise I received the missing on X error statement.
Given this,is this output and conclusion then fine for interpreting these latent classes? Thank you so much for your help!
Bengt O. Muthen
posted on Saturday, October 24, 2015 - 8:13 am
I have to see the full output to say - send to Support along with your license number.
davide morselli
posted on Monday, February 08, 2016 - 6:34 am
I'm trying like a mad to change the reference category of the between-level latent class in a non-parametric two-level LCA as descripted in Henry & Muth�n's paper.
my syntax of the VARIABLE and MODEL sections is:
usevariables = TOLER PROT ;
cluster = cntry;
within = TOLER PROT ;
classes = cb (5) cw(3);
between = cb;
CW on CB ;
model cw:
I can change the level-1 class order using the model CW part, but I can't find where and how to specify it for CB.
thank you!
Koksal Banoglu
posted on Monday, February 08, 2016 - 11:08 am
Dear Dr. Muthen,
I am running a multilevel LPA model, akin to the model developed by Henry & Muthen's (2010). With your kind permission, I want to pose three questions about interpretation of my output with references to the main article.
1- The propability estimates of level-2 predictors over the level-1 latent class solutions (i.e. Table 3, Henry & Muthen, 2010) refer to "C#2 on [Level-2 predictor name]" statements in the output, right?
2- The effect of level-2 predictors over the level-1 latent class indicator intercepts (i.e. Table 4, Henry & Muthen, 2010) refer to estimates of "model constraints" such as "POP30, GRW30"?? Then what is the function of total effect variables (i.e. C2POPLOG, C2TOBGRW and C2POVLEV) in the output now that the significance and effect size of those would not reported in the article? Or, first we should check the significance of total effect (e.g. C2POP*LOG) and direct effect estimates (e.g. C2_POP) on the latent class factors and then we can report the effect size of individual cross-level variables (e.g. POP30)?
3- I use LPA with continuous indicators thus I interpret the linear regression outcomes. Should I pay an extra attention to any estimate while interpreting the output?
Thank you for your patience to read my message in advance. Now I cross my fingers for your answer.
Best regards.
Bengt O. Muthen
posted on Monday, February 08, 2016 - 6:28 pm
Please contact the first author about these questions. She's at Colorado State Univ.
davide morselli
posted on Tuesday, February 09, 2016 - 1:35 pm
do someone have any suggestion for the problem I posted above?
Bengt O. Muthen
posted on Tuesday, February 09, 2016 - 6:25 pm
Which Figure and Appendix model are you trying to use?
davide morselli
posted on Wednesday, February 10, 2016 - 12:16 am
my model is:
usevariables = TOLER PROT ;
cluster = cntry;
within = TOLER PROT ;
classes = cb (5) cw(3);
between = cb;
type = MIXTURE TWOLEVEL;
CW on CB ;
model cw:
and I would need to change the reference class of from CB#6 to CB#1. I know how to do it with the within-level classes (by fixing the means as in the example above) but I can't find what I should do for the between one
Bengt O. Muthen
posted on Wednesday, February 10, 2016 - 1:18 pm
It helps me if you connect your model to models numbered in Henry-Muthen.
davide morselli
posted on Thursday, February 11, 2016 - 5:30 am
that would be Model 4a at p.214 of the SEM article
Thank you in advance
Bengt O. Muthen
posted on Friday, February 12, 2016 - 2:57 pm
Use SVALUES in your original run to save the estimates. Then use them in a Starts=0 run where you switch the regression coefficients for CW on CB so that CB#1 values are given for the last CB class. You may also have to re-calculate the logit for CB called [cb#1] etc. You do that by first computing all the CB class probabilities from the logits as described in Chapter 14 and then switch the probabilities and then compute the new logits.
Corey Savage
posted on Sunday, February 14, 2016 - 9:25 am
With model 2 in table 1 in Henry and Muthen (2010), the parametric approach to a multilevel 3 class model, do I need the following in the syntax for a 2 class model? Would I just limit that to only "C#1"?
Bengt O. Muthen
posted on Sunday, February 14, 2016 - 5:17 pm
Yes, with 3 classes you have 2 random intercepts: c#1 and c#2. And you want them to be able to correlate.
davide morselli
posted on Monday, February 22, 2016 - 8:02 am
Hi Bengt,
sorry for bothering again, but it's still not clear how I can switch the regression coefficients for CW on CB so that CB#1 values are given for CB#5 (the last class) as I cannot mention the last class directly.
Bengt O. Muthen
posted on Monday, February 22, 2016 - 5:51 pm
Send your run with the original solution and your best attempt at switching the classes to Support along with your license number. Briefly describe where you get stuck.
Brian Knop
posted on Monday, March 07, 2016 - 2:26 pm
I have looked through the user guide and Henry and Muthen (2010), but can't figure out how to get odds ratios for level 2 variable effects on latent classes (such as effect of tobacco growing state on smoking type). I can get coefficients (for level 2 variables), but not odds ratios.
Thank you.
Linda K. Muthen
posted on Monday, March 07, 2016 - 2:39 pm
The categorical variables are random intercept on level 2. So they are continuous.
Brian Knop
posted on Tuesday, March 08, 2016 - 8:23 am
Thank you for your quick response. That explains why the output gives odds ratios for within-level effects, but not between-level effects on the latent classes. But Henry and Muthen (2010) present between-level odds ratios, so it is possible, yes?
Linda K. Muthen
posted on Tuesday, March 08, 2016 - 9:30 am
The variable would need to be on the BETWEEN list and the CATGORICAL list to get an adds ratio on between.
Brian Knop
posted on Wednesday, March 09, 2016 - 9:17 am
Ok, for some reason I still can't get odds ratios when I do that. If I were hypothetically looking at school-level effects on latent classes of test scores and all variables used are categorical, my code looks something like this:
usevariables= schooltype mathscore engscore histscore;
categorical are schooltype mathscore engscore histcore;
between= cb schooltype;
classes=cb (3)
TYPE= mixture twolevel;
cb#1 cb#2 ON schooltype;
Would that produce odds ratios in the output?
Linda K. Muthen
posted on Wednesday, March 09, 2016 - 10:53 am
Please send the output and your license number to
Miatta Echetebu
posted on Wednesday, June 15, 2016 - 3:52 pm
We are trying to run a two-level LCA. The syntax we are using is
NAMES ARE ID agency directservices ServYouth TimeWork gender age RaceBWO education fieldstudy sector RacePriv InstDisc BlatantRace ;
MISSING are all (999);
USEVARIABLES = RacePriv InstDisc BlatantRace ;
tech11 tech14 ;
Our output AIC and BIC are nearly identical to the AIC and BIC we received when not running it with the second level. Additionally, the output gives us within-level variances but not between-level variances. Is this syntax correct for running a multilevel LCA? Is it actually running it with two levels or just reproducing the single level output?
Thank you very much for your help!
Bengt O. Muthen
posted on Wednesday, June 15, 2016 - 5:39 pm
You have to mention the random intercepts for the latent class variables on Between. For an example, see UG ex 10.6.
posted on Monday, August 15, 2016 - 9:48 am
Hello Bengt and Linda:
I have a multilevel LPA, with events (Level-1) nested within people (Level-2). Currently, I have a model with 8 within-person profiles, and nothing being specified at the between-person level of analysis.
In traditional multilevel research with a similar structure (events nested within people), it is common to group-mean center the L1 constructs prior to analyses. Would you recommend group-mean centering the L1 variables being specified as profile indicators? Would other centering decisions, such as grand-mean centering or even standardizing the profile indicators within-person, be appropriate?
Any guidance is greatly appreciated!
Bengt O. Muthen
posted on Monday, August 15, 2016 - 1:14 pm
I would not do any centering or standardization for this model.
Fang Fang
posted on Sunday, April 16, 2017 - 12:12 pm
Dear Drs. Muthen:
I am trying to run a two-level LCA. The syntax is
Names are
ID conflict CID fcontact pcontact live mpc mcp inpc incp emoclose;
missing are .;
USEVARIABLES = live fcontact pcontact mpc mcp inpc incp emoclose conflict ID;
CATEGORICAL = live fcontact pcontact mpc mcp inpc incp emoclose conflict;
CLASSES = c (3);
Analysis: TYPE = TWOLEVEL MIXTURE;
c#1 c#2;
Output: TECH11 TECH8;
However, the output doesn't show the "RESULTS IN PROBABILITY SCALE". Is there anything missing in my syntax to run a two-level LCA? I am using Mplus 6.12.
Thank you so much for your help!
Linda K. Muthen
posted on Monday, April 17, 2017 - 9:14 am
If we don't give it automatically, it is not available.
mohammad ahmadi
posted on Thursday, August 24, 2017 - 1:30 am
Hi Dear Dr. Bengt\Linda Muthen
I want to run a two-level bi-factor IRT model with random effects.
1. Is this the right syntax?
2. How do I calculate the effect of the clustering factor, for example gender? Or Is the gender impact significantly different from zero?
VARIABLE : NAMES ARE gender lang i3-i148;
USEVARIABLES ARE i3-i27;
CATEGORICAL ARE i3-i27;
MIssing are all (9);
cluster= gender;
TYPE =twolevel random;
estimator = ML;
MODEL: %within%
G by i3-i27;
F1 BY i3@
i4-i15 (4-15);
f2 by
i17-i27 (17-27);
G with
F1 with
G by i3-i27;
F1 BY i3@
i4-i15 (4-15);
f2 by
i17-i27 (17-27);
G with
F1 with
Best regards
Muhammad ahmadi
Bengt O. Muthen
posted on Thursday, August 24, 2017 - 6:50 pm
Try it and if you don't get what you want, send to Support along with your license number. Or ask on SEMNET.
Michelle Roley-Roberts
posted on Saturday, December 02, 2017 - 8:10 am
I am trying to run a 1-2-1 multi-level mediation model and have variables that are both between level and within level, thus I did not specify them in the BETWEEN ARE or WITHIN ARE statements.
When I run my syntax I get this error:
*** ERROR in MODEL command
Observed variable on the right-hand side of a between-level ON statement
must be a BETWEEN variable. Problem with: QOLITOT
*** ERROR in MODEL command
Observed variable on the right-hand side of a between-level ON statement
must be a BETWEEN variable. Problem with: LFQTOT
When I added those variables to the BETWEEN ARE statement, I then got this error:
*** ERROR in MODEL command
Observed variable on the right-hand side of a within-level ON statement
must be a WITHIN variable. Problem with: QOLITOT
*** ERROR in MODEL command
Observed variable on the right-hand side of a within-level ON statement
must be a WITHIN variable. Problem with: LFQTOT
Please advise.
Thank you!
Bengt O. Muthen
posted on Saturday, December 02, 2017 - 9:56 am
Send your full output to Support along with your license number.
Jilian Halladay
posted on Friday, April 26, 2019 - 2:20 pm
Hello Dr. Muthen,
I am doing a multilevel latent profile analysis (students within classes within schools) but I only want to identify the profiles at the individual level (while accounting for the sampling design).
Is this the correct code?
idvariable is studID;
type=mixture complex;
! no within or between statements
The output for this code provides summary data identifying the correct number of schools but the model output is modeling solely at a single level. In this case, am I getting a model that is adjusted for school? Or am I incorrectly coding for a 2 level (student within school) model?
When I change it to:
cluster=ischl studID;
within=v1 v2 v3 v4 v5 v6 v7;
I get almost identical loglikelihoods (-143857.684 one cluster and -143848.173 two cluster), similar AIC/BIC/LRT, and identical class counts and proportions of posterior probabilities and entropy. Since I only specified indicator variables at the individual level, is this model and the former similarly adjusting for schools?
If I want to also include class, it states a threelevel model is not possible for LPA. Is there another way to also account for a third level?
Thanks again for all your help
Bengt O. Muthen
posted on Saturday, April 27, 2019 - 6:20 am
I would use Type = twolevel complex where
cluster = idschl idclss;
So level 1 is student, level 2 is classroom, and the complex part is school.
See the Cluster option on page 621 in the UG.
Jilian Halladay
posted on Thursday, May 02, 2019 - 9:16 am
Great - thank you so much! That worked.
posted on Wednesday, May 29, 2019 - 7:02 am
I am conducting MLCA. What is the procedure to assign units at Level 2 to the most likely class at Level 2 based on the latent class posterior distribution? Would you please provide me with the example of Mplus code?
Thank you
Tihomir Asparouhov
posted on Wednesday, May 29, 2019 - 4:26 pm
You can use User's guide example 10.5 to see how this works. Add the following command:
savedata: file=1.dat; save=cprob;
Take a look at the SAVEDATA INFORMATION section in the output file. The classification variable for the cluster would be CB and you can find those values in the saved data file 1.dat.
posted on Tuesday, August 13, 2019 - 12:36 pm
I am conducting LPA and the clustering variables come from different classrooms (nested data). However, the number of cluster is only 6. In this case, I don't think MLPA is appropriate? In this case, what I can do to address the nested data structure? Thanks.
Bengt O. Muthen
posted on Tuesday, August 13, 2019 - 5:48 pm
You have too few clusters for MLPA. Use 5 dummy variables as covariates.
posted on Tuesday, August 13, 2019 - 6:48 pm
Thank you, Muthen!
I am wondering if the following two codes are both correct for including 5 dummies as covariates in LPA:
VARIABLE: NAMES = u1-u4 dum1 dum2 dum3 dum4 dum5;
CLASSES = c(3);
AUXILIARY = dum1-dum5 (R3STEP);
DATA: FILE = 3step.dat;
VARIABLE: NAMES = u1-u4 dum1 dum2 dum3 dum4 dum5;
CLASSES = c(3);
c#1-c#2 on dum1-dum5;
DATA: FILE = 3step.dat;
Bengt O. Muthen
posted on Wednesday, August 14, 2019 - 6:40 am
They are correct. (1) is 3-step and (2) is 1-step. See also the appendix of our web note 15:
posted on Wednesday, August 14, 2019 - 11:04 am
Thank you, Muthen!
One follow-up question: I found that the LPA results are identical for LPA without dummies (without controlling for clustering effects) and LPA with dummies using R3STEP. Is this normal? I thought bringing in dummies as covariates should somehow change the LPA solution to some extent.
Bengt O. Muthen
posted on Wednesday, August 14, 2019 - 5:11 pm
Yes, it is the point of R3STEP that they are the same - read web note 15.
Covariates do change the LPA solution when you don't do 3-step like R3STEP.
posted on Thursday, August 15, 2019 - 1:33 pm
Thank you, Muthen!
1. So, I guess if my goal is to using covariates (i.e., dummies) to control for the nested data structure, 1-step approach is preferred since I want LPA solutions to account for the clustering effect. Am I right?
2. I am wondering why we specify the model by adding paths from dummy variables to the latent factor (i.e., c on dum1-dum5) but not to the clustering indicators (u1-u4 on dum1-dum5). Isn't the indicators are the dependent variables, and in fixed effects models, dummies are adding as predictors of dependent variables?
Thank you!
Bengt O. Muthen
posted on Thursday, August 15, 2019 - 5:22 pm
1. Yes.
Q2: C on dum1-dum5 implies that the dummies influence the indicators indirectly via c. This is a fundamental aspect of the model. You cannot identify both c on dummies and indicators on dummies.
posted on Thursday, August 15, 2019 - 8:46 pm
Thank you, Muthen! This is really helpful.
Katherine Paschall
posted on Tuesday, July 21, 2020 - 8:47 pm
Hello, I am trying to estimate a multilevel LPA with two indicators at the student level (level 1) and two indicators at the classroom level (level 2). I would like the profiles to be estimated at the student level. I'm confused about how to appropriately estimate this model:
1) which example or reading is most helpful? I have tried to read every example and paper mentioned in this thread and none are providing clarity.
2) it makes sense to me to add covariances between the level 1 indicators (at the within level) and then between the level 2 indicators (at the between level), but cannot figure out the latter.
I appreciate your help.
Bengt O. Muthen
posted on Thursday, July 23, 2020 - 8:35 am
1) The Henry-Muthen multilevel LCA paper is closest.
2) Use WITH at both levels.
If this doesn't help, send your output to Support along with your license number.
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•Assist in the development and implementation of vision, strategies, and tactics to maximize the departments effectiveness while minimizing costs
•Review statistical data of various systems in order to verify accuracy and timely processing
•Ensure internal controls are appropriate and develops policies and procedures and ensures compliance with government regulations and customer contracts
•Provide counsel to senior management
•Work with other areas for solutions to complex problems
•Participate in critical interactions with both internal and external customers
•Hire, train, coach, counsel, and evaluate performance of direct reports
•Seven or more years' experience with Health Insurance / Payer operations, Payment Integrity, reporting, audit guidelines, and process improvement required
•Experience with complex business environments including multiple entity and highly automated situations required
•Five or more years' management experience; or any combination of education and experience which would provide an equivalent background, required
•Expertise developing and translating business requirements to IT required
•Expertise developing / leading the development of ad hoc and routine reporting required
•Knowledge of / experience with Hadoop preferred
Anthem, Inc. is ranked as one of America's Most Admired Companies among health insurers by Fortune magazine and has been named a 2019 Best Employers for Diversity by Forbes. To learn more about our company and apply, please visit us at careers.antheminc.com. An Equal Opportunity Employer/Disability/Veteran.
Anthem, Inc.
- Anthem, Inc. Jobs


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Some good history in this interview.
http://www.the-monitors.com/2013/07/12/ ... rl-bartos/
The music of futurism, which started in Italy at the beginning of the 20th century with Marinetti, turning to Paris where Pierre Schaeffer was calling it 'musique concrete', then going to Cologne where Karlheinz Stockhausen moved it on and composed 'Gesang der Jünglinge'. It was really part of our German heritage. Karlheinze Stockhausen! Musique concrete! And pop music! And Lou Reed! And The Beatles! All rolled into one. Dead on! And I didn't have to change my suit. When I came out of the opera in my suit – I was playing at the opera to make some money – I went into the Kling Klang studio and I didn't have to change!
In terms of rhythm, what other musicians were important to you?
Stravinsky. You know the piece 'Le Sacre Du Printemps'? Every bar he's changing the meter. So if you have a look at the score it has seven 8ths, three 8ths, 16ths, 4/4 – it's changing constantly, you never get in. So he made it a concept, he wanted to have this machine music.
EM History: Interview Karl Bartos
Discuss musical topics that are not directly 808 State related.
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About Diamond Direct Buy
How to Order
Mission Statement
Customer Testimonials
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Diamond Engagement Rings
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Loose Diamonds
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Mens Watches
Custom Jewelry
Diamond Blog
Customer Area
Contact Us
how to buy a diamond
About Me
Let me introduce myself I'm a Private Jeweler based in Chicago USA, I moved to the USA in 2000 from Melbourne Australia, when I met my now husband,we've been together over 18 yrs married with 2 sons.
I have been in the Diamond Industry over 16 years. During this time I have established long lasting trusted relationships with diamond exporters and suppliers from around the world. I have a passion for helping you buy the ring of your dreams. I LOVE WHAT I DO , My mission is to help you come up with the most beautiful ring at the best possible price. I everyone says that, all I ask is "give me a chance" visit my site, browse around and see my videos and photos, compare MY prices to any store or wholesaler you may be considering. I can make ANY style you can show me. One thing I can promise,
If I don't like the diamond
. I will NOT sell it to you. My suppliers know know how picky I am.
All my rings are CURRENT HOT styles and ALL my diamonds are 100% Natural and Certified. *CE diamonds available by request. If you do not see specifically what you are interested in "No problem". It is impossible for me to list a photo of every style out there BUT NOT impossible to get it made for you. Most rings take us 7-10*days to make, so the process is fairly fast. Please email me with details and if possible a link to a style of setting you like. I will get back to you with a few options. My goal is to make her eyes POP when she sees the ring....not your Life savings buying one. You can read my references below. I deal mainly with Direct Wire Payments, with a Written Purchase Agreement outlining your purchase, where there are no additional fees. or you can your Credit Card for a small 3% processing fee. All sales have a written Purchase Agreement , Any way you pay there is ALWAYS 7 Days inspection
DATE TO YOU . This allows you time to see it, have it verified or appraised independently and make your decision. I have customers who purchased from me all around USA, Canada, UK , France, Poland, Russia, Australia, New Zealand, Morocco, Egypt and many other places.
Anna D. /Owner
Diamond Direct Buy LLC.
"I Love SAVING you Money on Diamonds
Any SHAPE-SIZE & STYLE
Call 312- 388-ANNA(2662)
Find me on these social media outlets:
DiamondDirectBuy -Anna
Linked In Profile and References
Wedding Wire Reviews
I use escrow.com as payment
*CE means ( CLARITY ENHANCED
Contact Diamond Direct Buy
Mission Statement & IMPORTANT INFORMATION
Hi I'm Anna Diamond Direct Buy LLC is a company based in Chicago Illinois, USA. In Business since 2006 in USA. I moved to the USA since 2000 from Melbourne Australia.
My business philosophy is simple.
"I hope to provide my clients with great value for money by ensuring my rings are of the highest quality and at the lowest price sold DIRECT to you"
There are no store mark ups NO MIDDLEMAN , NO STORE OVERHEAD added to the cost, will save THOUSANDS.
To achieve this goal :
1. I hope to educate my clients so they make an informed selection
2. Provide only certified diamonds that are INDEPENDENTLY Certified GIA , HRD, AGS , IGI, and EGL-USA or EGL IF REQUESTED.
3. Keep my costs low and margins to the minimum to ensure you get the best price.
4. At all times I will maintain integrity in doing business with you, as my reputation, and satisfied clients are the best form of promotion for my business. I love what I do .
I am ALWAYS looking for deals, just like you are. I buy my diamonds and pay up front for the best options available from exporters to me, therefore my suppliers are able to give me much better prices because they don't have to wait months for their money.
As a result, I get first pick and better quality for much less than the other stores that pick and choose and pay later on Memos. I have NO overhead ( you don't end up paying for my rent, staff, insurance, inventory and other bills in YOUR PRICE that are associated with running a store).
I operate this site myself and work on a VERY LOW margins. This ALL adds up to a OFFERING YOU GREAT OPTIONS AND HUGE savings.
I believe that buying a diamond should be an exciting experience. It can also be stressful and confusing, by allowing me to be a part of this special occasion in your life.
I will ensure that your experience is a memorable one. I have induced basic information on diamond 4 C;s as well as Certification grading report differences. Everything is as transparent as possible.
Future referrals from my customers are the biggest complement I can get. I also encourage you to visit the GIA website to educate yourself about the 4 C's or google information about diamond that is easily available online.
I am not a gemologist I serve as a direct " Broker"on your behalf. I buy already polished diamond that are accompanied with a Lab Grading report from various labs.
All Diamond Laboratories who do diamond grading reports, use "their own "grading scales and criteria, they DO DIFFERED from each other, as there is NO ONE SET STANDARD in the industry ( GIA has the opinion of being the strictest and most reliable ) however even they do not offer any guarantee.
Certain aspects are "subjective" opinion of the expert and will vary from one to another, especially but not limited to color and clarity even though they use the same terminology, which may be confusing.
Laboratories who pre grade these diamonds offer no guarantee or value of the diamond. Diamond Direct Buy LLC does not agree or disagree with any reports and does not offer any grading input I mainly rely on their information provided on the report, The price is calculated on the acquisition cost for each diamond
plus the manufacture cost for the setting to determine the price for each piece.
When you buy from me, you always have
3 days inspection from when the item is delivered to you
to get a second opinion or appraisal and make a final decision then.
***Only some custom orders on mountings are not refundable however the center DIAMOND is ALWAYS refundable if you let me know within 3 days of receiving it.
Looking forward to working with you. call me 312-388-2662 or email
Conflict Free Diamonds
All diamonds purchased at Diamond Direct Buy LLC are from legitimate sources not involved in funding conflict and in compliance with United Nations resolutions. I guarantee that the diamonds I purchase on your behalf are conflict free, based on personal knowledge and/or written guarantees provided by my suppliers.
For more information on conflict diamonds, please visit
Waiver and Release of ALL claims
Please read this carefully and be aware that in purchasing a diamond or a engagement ring from Anna/ Diamond Direct Buy LLC you are using a "DIAMOND BROKER" offering you different options within your budget. It is agreed and accepted by the "BUYER" that Anna /Diamond Direct Buy LLC assume no liability or responsibility for the diamond grading you have chosen.
I strongly encourage all my customers to educate themselves about the 4 c's
as well a different Grading reports available out there AS THEY ARE NOT ALL THE SAME.
Some big names are GIA, EGL-USA, AGS, IGI and HRD
Before any purchase is finalized. It is common knowledge that there are many different certifications available however, they are NOT all equal. Although GIA has the "OPINION" of being the most strict and consistent, even they do not offer any guarantee or warranty on their Grading report NO DIAMOND REPORT DOES.
Diamond Direct Buy acknowledge that SOME EGL International LABS have closed in Europe in 2014. However EGL Platinum and EGL Hong Kong are still open today and offered for sale to customers, via stores, ebay and online.
Mostly with EGL-HONG KONG Certification which could be grades off to GIA COMPARISON using the same Letter Grading and Clarity Terminology. There are no 2 diamonds alike, and it can not be generally said that they are all off 1 or 2 grades always. Some diamonds could be graded many grades off on color and clarity, some less , It all depends on the EACH diamond.
Grading is
and it is the opinion of the LAB the equipment, and personal training used to determine the what cut, color clarity, polish and symmetry it receives. Two diamonds with the same color and clarity CAN still look very different. Diamond Direct Buy does not offer a gemological opinion of any kind. I do offer you a transparent transaction, great prices and inspection period so YOU can see it, have it independently verified, before you make a final decision.
Once the inspection period ends and sale becomes FINAL . You are solely responsible in participating in the purchase You FULLY understand and accept assumption of all risk and waive and release all claims towards Anna and or Diamond Direct Buy LLC by sending payment to complete a purchase transaction. ALL SALES HAVE A
TO HAVE THE DIAMOND/RING VERIFIED BY A 3rd PARTY, APPRAISER OR JEWELER IN YOU R AREA THEN THE SALE IS FINAL.
ALL SALES HAVE A WRITTEN PURCHASE AGREEMENT AND EMAIL TYPED IN SIGNATURE will have the same effect as a original form signature.
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- What Is Tenofovir?
- Who Should Take Tenofovir?
- What About Drug Resistance?
- How Is Tenofovir Taken?
- What Are the Side Effects?
- How Does Tenofovir React With Other Drugs?
What Is Tenofovir?
Tenofovir (Viread), also called bis-POC PMPA, is a drug used as part of antiretroviral therapy (ART). It is manufactured by Gilead Sciences. The FDA approved tenofovir for use against HIV in October 2001. Generic versions have been tentatively approved under PEPFAR (see Fact Sheet 475).
Tenofovir is a nucleotide analog reverse transcriptase inhibitor, or nuke. These drugs stop HIV from multiplying by preventing the reverse transcriptase enzyme from working. This enzyme changes HIV's genetic material (RNA) into the form of DNA. This has to occur before HIV's genetic code is inserted into an infected cell's genetic codes.
Who Should Take Tenofovir?
Tenofovir was approved in 2001 as an antiretroviral drug (ARV) for people with HIV infection. In 2010 it was approved for use by people between 12 and 18 years old. In 2011 it was approved for use in children ages 2 to 12. It has not been carefully studied in people older than age 65. In US treatment guidelines (see Fact Sheet 404), tenofovir is listed as a preferred drug for people just starting ART.
There are no absolute rules about when to start ART. You and your health care provider should consider your CD4 cell count, your viral load, any symptoms you are having, and your attitude about taking ART. Fact Sheet 404 has more information about guidelines for the use of ARVs.
Be sure to let your health care provider know if you have any kidney problems. People with kidney damage may need to take a reduced dose of tenofovir.
If you take tenofovir with other ARVs, you can reduce your viral load to extremely low levels, and increase your CD4 cell counts. This should mean staying healthier longer.
Tenofovir may also help control Hepatitis B. However, Hep B got much worse in some people who were taking tenofovir and then stopped taking it. Get tested for hepatitis B before you start taking tenofovir to treat HIV. If you have hepatitis B and stop taking tenofovir, your health care provider should carefully monitor your liver function for several months.
Tenofovir is also being studied for the prevention of HIV infection. Gilead hopes that just one pill a day will be effective.
What About Drug Resistance?
Many new copies of HIV are mutations. They are slightly different from the original virus. Some mutations can keep multiplying even when you are taking an ARV. When this happens, the drug will stop working. This is called "developing resistance" to the drug. See Fact Sheet 126 for more information on resistance.
Sometimes, if your virus develops resistance to one drug, it will also have resistance to other ARVs. This is called "cross-resistance." However, tenofovir seems to have very little cross resistance with other ARVs.
Resistance can develop quickly. It is very important to take ARVs according to instructions, on schedule, and not to skip or reduce doses.
A benefit of tenofovir is that it works against several strains of HIV that are already resistant to AZT or ddI.
How Is Tenofovir Taken?
The normal adult dose of tenofovir is 300 milligrams (mg) taken as one pill, once a day, with or without a meal. People who are taking both tenofovir and ddI (didanosine, Videx) should take tenofovir 2 hours before, or one hour after didanosine. A prodrug of tenofovir, GS7340, is being developed. When it breaks down in the body, it produces tenofovir. In early studies it is much more potent than tenofovir and may have fewer side effects. Children ages 2 to 5 will use a powder formulation. For children ages 6 to 12, there are pills of 150 mg, 200 mg, 250 mg. Dosing is based on age and weight.
Tenofovir is also available in Truvada, a combination of tenofovir and emtricitabine. See Fact Sheet 421 for more information.
What Are the Side Effects?
With the start of any ART there may be temporary side effects such as headaches, high blood pressure, or a general sense of feeling ill. These side effects are likely to get better or even disappear over time.
The most common side effects of tenofovir are nausea, vomiting and loss of appetite. Tenofovir can ause kidney damage. Creatinine levels should be monitored in people taking tenofovir. Tenofovir can also damage the liver. People taking tenofovir should have their liver health monitored.
Tenofovir can reduce bone mineral density (see Fact Sheet 557). Calcium or vitamin D supplements may be helpful. This is especially true for people with osteopenia or osteoporosis. This is important for young people because bone density normally increases during this period.
How Does Tenofovir React With Other Drugs?
Tenofovir can interact with other drugs or supplements you are taking. These interactions can change the amount of each drug in your bloodstream and cause an under- or overdose. New interactions are constantly being identified. Make sure that your health care provider knows about ALL drugs and supplements you are taking.
Tenofovir results in higher blood levels of didanosine (Videx). ddI and tenofovir should not be used together, especially in patients with a high viral load and a low CD4 count. Serious ddI side effects may result.
Tenofovir blood levels increase if it is taken with the protease inhibitors atazanavir (Reyataz) and lopinavir/ritonavir (Kaletra). This can increase the risk of tenofovir side effects. Tenofovir decreases blood levels of atazanavir. Ritonavir should be taken when atazanavir is taken with tenofovir.
Tenofovir does not affect blood levels of methadone, ribavirin or adefovir. There is no known interaction between tenofovir and buprenorphine.
Three regimens should normally not be used without careful analysis or extra ARVs:
- Tenofovir (Viread) + abacavir (Ziagen) + lamivudine (Epivir)
- Tenofovir (Viread) + didanosine (Videx) + lamivudine (Epivir)
- Tenofovir + Videx EC + either efavirenz or nevirapine in patients new to ART with high viral loads.
Tenofovir is eliminated by the kidneys. It is not metabolized in the liver, so it is not expected to interact with many other drugs. However, medications with names that end in "-ovir," such as acyclovir and ganciclovir, may interact with tenofovir.
Tenofovir should be used as part of combination antiretroviral therapy (ART) against HIV. It is normally used along with a nucleoside analog reverse transcriptase inhibitor (nuke) plus a non-nucleoside reverse transcriptase inhibitor (NNRTI) or a protease inhibitor.


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Photographer's Note
Tyre was founded at the start of the third millennium BC. Tyre originally consisted of a mainland settlement and a modest island city that lay a short distance offshore. But it was not until the first millennium BC that the city experienced its golden age.
In the 10th century BC, King of Tyre, Ahiram also known as (Hiram), joined two islets by landfill. Later he extended the city further by reclaiming a considerable area from the sea and built two ports and a temple to Melkart, the city's god. Phoenician expansion began about 815 BC when traders from Tyre founded Carthage in North Africa.
Eventually its colonies spread around the Mediterranean and Atlantic, bringing to the city a flourishing maritime trade.
For more images please visit www.romancolonnades.com
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Photo Information
- Copyright: Hussein Kefel (Hussein_Kefel) (825)
- Genre: Places
- Medium: Color
- Date Taken: 2010-10-03
- Categories: Architecture, Ruins
- Camera: canon eos 7d, Canon EF 18-200mm
- Exposure: f/10.0, 1/250 seconds
- More Photo Info: view
- Photo Version: Original Version
- Date Submitted: 2011-03-12 9:20
- Favorites: 1 [view]


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"Every physical thing you could ever imagine in one week and so it was a gauntlet. The X-Gamer took over in my head and I went 'I'm going to go for this,'" Carrey told Early Show correspondent Hattie Kauffman.
"Even when I was doing the bungee jump, they were still tender and I was thinking 'Am I going to pull my ribs apart by doing this bungee jump?' And then I was thinking about actual death. It was like, 'Oh, I could be crossing over here,'" Carrey admitted.
"Yes. I believed in myself from the get go. I was trying to get on as a regular and I got a letter back from "The Carol Burnett Show" saying 'We hire our talents by agencies, but we wish you best of luck and it's pretty amazing that a 10-year-old can do 150 impressions.' All I cared about was that I got a letter from Hollywood," he said.
"I definitely have reached him on the level of friendship between us and doing Star Wars imitations and he is really into it. He loves being Darth Vader and he loves when I am the emperor. 'Luke Skywalker! Talk to Luke Skywalker!' I tell him to choose the dark side of the force," he joked.
"Yes. Absolutely. But, you know, I don't believe in backfires. I believe that everything we do is for a purpose. I've said yes to some funky things, absolutely, that I go, 'That's going to be with me for a while. Stain! Going to call it a UFO!' It follows you for years afterwards," he said.
"I'll do it. I don't care. I'm not afraid. I'm not afraid to cross dress. We were out there for the day and there were so many paparazzi around I immediately said 'Give me the bathing suit. Give me the bathing suit.' She goes, 'What, are you kidding me?' I said 'No, give me the bathing suit. I'm ready for this. I've been working, doing some crunches.' Thank God she has a sense of humor that she was actually willing to walk with me in that thing. Yeah, we got -- we got a lot of attention for that." he admitted.
http://www.cbsnews.com/stories/2008/12/ ... nt_4665301


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Energy 101: Electric Vehicles
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Text Version
Below is the text version for the Energy 101: Electric Vehicles video.
The video opens with "Energy 101: Electric Vehicles." This is followed by various shots of different electric vehicles on the road.
Wouldn't it be pretty cool to do all of your daily driving without ever having to fill up at a gas station? Well, that's quickly becoming a reality for people who drive electric vehicles—sometimes called EVs.
EVs are gaining popularity. And with good reason—they're convenient; they're sleek and quiet; they keep our air clean. And for most of the short-distance driving we do, they're the perfect way to get from point A to point B safely, reliably, and comfortably.
Text appears onscreen: "80% of Americans drive less than 40 miles round trip for their daily commute."
Okay, have a look at the numbers. More than 80% of Americans drive less than 40 miles round trip for their daily commute, which is just right for an EV.
The video moves to shots of EVs on the road. One EV's trunk is opened to show its battery compartment.
Many of today's electric cars can go up to 100 miles on a single charge. That's because battery technology continues to advance, becoming smaller while storing more energy.
Another EV's hood is opened. Text appears onscreen: "EVs – Powered by Lithium Ion Batteries."
Lithium ion batteries—like the ones in cell phones—are a big reason for that improvement.
The video shows a shot of an EV on the road, then a shot under the hood of an EV. Text appears onscreen: "Up to 80% of Energy Transferred."
Here's how an EV works. Batteries transfer energy to an electric motor. The motor turns a drive train that turns the wheels. It's a highly efficient technology: up to 80% of the batteries' energy is transferred directly to power the car.
The video shows a hand navigating the electronic display of an EV, and then that of a mobile phone.
Everything is computer controlled, and a display shows you how the car is performing. The display lets you know about how much battery power you have left, and if you need to find a place to recharge, new software built into the car—or on your mobile device—will guide you to the nearest charge point.
The video shows an EV's power port opening; a power supply is plugged in to charge the battery.
When you're ready to charge your EV's battery, instead of a gas tank, there's a power port. And instead of refueling, you recharge. Just plug it in!
The video shows an EV being charged at a public charging station.
Most people will probably recharge overnight when they're done driving for the day and electricity may be cheaper. But for a quick charge during the day, charging stations are popping up in thousands of convenient community locations across the U.S.
The video shows various shots of an EV: the vehicle in motion, its display screen showing its battery power status, and its power port being charged.
Check out this extended range EV. It starts by using battery power, but when the battery power runs low, a gasoline-fueled engine kicks in to power the electric motor, which in turn drives the wheels. So for shorter trips, you can rely on electricity, and still take longer road trips whenever you want. Anywhere you go, you can simply plug in or fill up.
The video shows various shots of EVs on the road.
EVs have a lot of great advantages: cleaner air, lower maintenance costs, and they help reduce America's dependence on foreign oil.
America has had a long love affair with cars. Now, we're starting the next chapter—this time falling for clean, comfortable, convenient electric vehicles.


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- Software
- Data Portals
- User Support
- Resources
- About Us
02/12/2013 - 12:00pm
Mesa Lab, Vislab
Michael Scheurer, University of Heidelberg
In order to represent forecast uncertainty in numerical weather prediction, ensemble prediction systems generate several different forecasts of the same weather variable by perturbing initial conditions and model parameters. The resulting ensemble of forecasts is interpreted as a sample of a predictive distribution. It offers valuable probabilistic information, but often turns out to be uncalibrated, i.e. it suffers from biases and typically underestimates the prediction uncertainty. Methods for statistical post-processing have therefore been proposed to re-calibrate the ensemble and turn it into a full predictive probability distribution.
Weather variables like temperature depend on factors that are quite variable in space which suggests that post-processing should be done at each site individually. If a predictive distribution is desired at locations where no measurements for calibration are available, post-processing parameters from neighboring stations must be interpolated. We propose an extension of the non-homogeneous Gaussian regression (NGR) approach for temperature post-processing that uses an intrinsically stationary Gaussian random field model for spatial interpolation. This model is able to capture large scale fluctuations of temperature, while additional covariates are integrated into the random field model to account for altitude-related and other local effects.
In the second part of this talk we discuss the modeling of spatial correlations of forecast errors for temperature. This becomes important whenever probabilistic forecasts at different sites are considered simultaneously, or when the interest is in composite quantities like averages, minima, or maxima of temperature over some domain. Again, we use Gaussian random field models which are now fitted to forecast errors in a training data set, and permit the simulation of re-calibrated temperature fields with corrected spatial correlations.
Both of these spatial aspects are illustrated with temperature forecasts by the COSMO-DE-EPS, an ensemble prediction system operated by the German Meteorological Service, and observational data over Germany.
Tuesday, February 12, 2013 - 12:00pm
Location: Mesa Lab, Vislab


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Greater Boston
Convention & visitors Bureau
We are celebrating our 28th year! Great Back bay location, walking distance to Hynes Convention Center, Fenway Park, Copley Square, Newbury Street, Boston Common and other attractions such as, museums, restaurants, shopping, nightlife and historic sites. Free WiFi and internet station. We serve continental breakfast and parking is available. We are a non smoking property, with outside decks all for a great price. For more information visit our website or call us toll free. You can also view our other location at www.oasisgh.com.


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Jim Jones Doesnt Know Theirs A Parody Video For "Pop Champagne" Dancing To "Girls Just Want TO Have Fun": Angie Martinez Brings That To Jim's Attention. Well Heres That Parody Video
Angie Martinez letting Jim Jones know about the champagne parody video and the footage. We dont know who created that footage or why
Please click the "Report" button below if the video on this page is not working properly.
Comments will only be displayed by verified emails. No Spamming or Racism.


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East Hampton delays code violation fine increases
East Hampton officials want to drastically raise fines for code violations including beach driving and littering, but delayed action after a complaint that penalties and late fees would be too steep.
The town board decided last week not to vote on the plan after David Buda of Springs took issue with the time limits on paying the penalties.
"This is a late fee that is so onerous that you double the fine if they do not respond in 15 days," Buda said. "If you lose a ticket, it triples after 30 days. . . . It's $800 for driving with no permit on the beach. Is this the message we want to give to visitors from afar?"
That beach driving fine is one of the steepest proposed by the town; it starts with a $250 ticket. The $100 littering ticket would increase to $350 if unpaid after 90 days, and the $200 fine for discharging fireworks without a permit would go to $650 if not paid after 90 days.
Repeat offenders already face even stiffer fines. Anyone who violates the East Hampton Town shellfish code three times within 18 months faces a fine of up to $1,500 and up to 20 days in jail, as well as the loss of their shellfish permit.
Town Attorney John Jilnicki said that while the penalties proposed for not paying tickets on time might be steep, they are regularly waived in Town Justice Court if people show there was a good reason for them not to respond in a timely way, such as being in a hospital or being out of town.
Buda argued that just getting to town justice court on a weekday can be difficult for someone living in Manhattan, and relying on the Postal Service to pay a ticket can result in enough of a delayed payment to subject someone to an additional fine.
Jilnicki explained that the town board was considering the change to take the ambiguity out of some of its fines, which can range widely. The minimum cash fine for the third violation of the shellfish code starts at $300 and can be as much as $1,500 at the judge's discretion.
The town board could amend the fine structure and pass it without another public hearing, Jilnicki said.


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Cutipol is a third-generation family run Portuguese company that focuses on trend-setting design elements with a no-compromise ethos when it comes to quality manufacturing techniques.
The precise, minimal lines of Cutipol's Goa line are effortlessly elegant and ergonomically pleasing (even to large hands). Goa is made of the highest quality 18/10 stainless steel in brushed finished with black resin handles. Handmade in Portugal.
Care: Dishwasher safe - to prevent corrosion of knife blades, do not leave inside the dishwasher after cleaning
If this item is out of stock, please allow 4-6 weeks for delivery.
Should you have any questions, please contact us directly at firstname.lastname@example.com or 416.926.1120 / 1.866.926.1120